The former Brexit Secretary, 72, said that his resignation in July 2018 was a 'strategic' move which he hoped would lead to Mrs May being replaced by a leader who would push through a harder Brexit.
The former Conservative party chairman plunged Mrs May's Government into turmoil when he quit over her Chequers Deal which would have tied the UK to EU rules for manufactured goods, food and farm produce in return for staying in the single market.
But he described his resignation as a 'necessary' move to ensure that the UK had a tougher Brexit under a new Prime Minister which would be 'a break point in history'.
David Davis (right) said he resigned from the government of Theresa May (left) to force her out
Speaking in a new Hanover Communications' White Swan podcast which discusses how business leaders can cope with a crisis, he told how he deliberately plunged Mrs May's Government into crisis after she sidelined him by drawing up her own soft Brexit plan.
Davis, a former Tory leadership candidate who spent two years as Secretary of State for Exiting the EU, accused Mrs May of caving in to EU demands for regulations in Northern Ireland to be the same as EU rules in the Republic of Ireland.
He said: 'The strategy was being dictated by Number 10 and my advice was simply not being taken from December 2017 when Theresa May gave in to the demand that Northern Ireland should be staying in line with southern Ireland.
'The European Union and the Irish Republic together insisted that the regulatory standards in the North should be the same as the South which then creates a problem between Northern Ireland and the rest of the UK.
'She gave in on that, without telling me actually, and then told me afterwards. At that point, I thought, 'This is going to go horribly wrong', and the most difficult time… was between that December and the subsequent July.'
Davis recalled how he tried to change the strategy by getting Mrs May to allow him to write a White Paper detailing his way forward to create a proper Brexit.
But he added that she then secretly drew up her Chequers Plan, and banned him from having any input into it
Davis said: 'I said give me a written version and I will go away and rewrite it to see if I will make it work.
Davis said he hoped that his resignation would force out Theresa May (pictured leaving Downing Street with husband Philip in 2019) and replace her with a Brexiteer leader
'Most of the time she did. To be fair to her in the two years we worked together, nine times out of ten, she did, but not this time.
'So on the Wednesday, when she said she wasn't going to move, I knew at that point that I had to do something different.
'I thought there was no way staying inside the Government (that) I could change this, but I new that the act of leaving would change it.
'Regrettably I thought it was 80 to 90 per cent probable that if I left, she would be gone a year later, and then somebody else would come along to do it properly, and I would have a say on who that someone else was.
'So that was a strategic move. The resignation was a strategic move to drive a change in strategy which we have got today.
'If nothing else, the fact that Brexit happened and happened properly, not keeping us inside the medicines agency for example, means there are hundreds if not thousands of people alive today because they have been vaccinated who would not have been otherwise.'
He added: 'It was very cold blooded. I took a long time over it. I could always see a few weeks ahead in this exercise, and by the time I got to July, I could see a year ahead.
'It's a very good demonstration of how sometimes you have to make a strategic break point in what is a tactical never ending loop.'